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Is there a methodology for calculating the co-solubility of two salts with different components?

For example, say I mix $\pu{200 g}$ of $\ce{MgSO4}$ into $\pu{1L}$ of water (solubility = $\pu{350g/L}$), then start mixing $\ce{NaCl}$ in also (solubility = $\pu{359g/L}$). Sodium sulfate (solubility = $\pu{139g/L}$) will be the first thing to precipitate out, but that doesn't tell us about the effect on $\ce{Mg^2+}$ and $\ce{Cl-}$ ion solubility. I would expect that the water activity would decrease because of the higher overall solute concentration, but I don't know a good way to quantify that.

If they had common ions, I could use Le Chatelier's principle and the solubility equilibrium constants to predict the solubility, but that's not relevant since all the ions are different.

I know I could use a group contribution method like LIFAC, but I was hoping there was a simpler first take?

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